Making one cone with cap out of a role paper of 12 cm in width. Cone has θ in center angle. Cap and cone have largest areas and each with one piece.
Find the minimum length, l(θ), of role paper required.
If θ=90deg, then l=15 cm is the answer.
I understand what you do. I just think its inconsistent to forbid making the cone larger than 12 cm side length (like in Lucs 45° solution) but accept to make it smaller for angles larger than 180°. Just my 2 cent.
I would rather stay with "largest surface but minimal paper" throughout or with constant side length 12 cm and minimal paper (which would allow only angles from 0 to pi.
Here a numerically derived solution for the latter:
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